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Chapter 7: Problem 53

Determine whether the statement is true or false. Justify your answer. Two angles and one side of a triangle do not necessarily determine a unique triangle.

Short Answer

Expert verified
The statement is false. According to the ASA rule (Angle-Side-Angle), two angles and one side can determine a unique triangle.

Step by step solution

01

Understanding of Statement

The given statement says that 'Two angles and one side of a triangle do not necessarily determine a unique triangle.' This means, according to the statement, given two angles and one side, there is still ambiguity about the triangle that is formed.
02

Apply the ASA (Angle-Side-Angle) Congruency Rule

According to the ASA Congruency Rule, if two angles and the side enclosed between them in one triangle are congruent to the corresponding angles and enclosed side of another triangle, they are said to be congruent. On applying Angle-Side-Angle (ASA) Congruency, two angles and one side can determine a unique triangle.
03

Conclude the Statement

Following the ASA Congruency rule, the given statement 'Two angles and one side of a triangle do not necessarily determine a unique triangle' is false.

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